An exponential decay function, and use it to approximate the population in 2027 is P(t) = 4001e^-(0.0037)(28) = P(t) = 4001e^-0.1036
Exponential equationThe standard exponential function is expressed as:
P(t) = P0e^-rt
P0 is the initial population = 4001r is the rate. = 0.37% = 0.0037t is the timeSubstitute
P(t) = 4001e^-(0.0037)t
If t = 28 (by 2027)
An exponential decay function, and use it to approximate the population in 2027 is P(t) = 4001e^-(0.0037)(28) = P(t) = 4001e^-0.1036
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A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the time that the rocket will hit the ground, to the nearest 100th of second.
y=-16x^2+64x+89
Step-by-step explanation:
I assume that "ground" is at 0 ft height. which is in an actual scenario not airways the case.
y = -16x² + 64x + 89
shows us that the tower is 89 ft tall (the result for x = 0, at the start).
anyway, if the original assumption is correct, then we need to solve
0 = -16x² + 64x + 89
the general solution for such a quadratic equation is
x = (-b ± sqrt(b² - 4ac))/)2a)
in our case
a = -16
b = 64
c = 89
x = (-64 ± sqrt(64² - 4×-16×89))/(2×-16) =
= (-64 ± sqrt(4096 + 5696))/-32 =
= (-64 ± sqrt(9792))/-32
x1 = (-64 + 98.95453501...)/-32 = -1.092329219... s
x2 = (-64 - 98.95453501...)/-32 = 5.092329219... s
the negative solution for time is but useful here (it would be the time calculated back to ground at the start).
so, x2 is our solution.
the rocket hits the ground after about 5.09 seconds.
Evergreen Corporation manufactures circuit boards and is in the process of preparing next year's budget. The pro forma income statement for the current year is presented below.
Sales $ 3,500,000
Cost of sales:
Direct Material $ 500,000
Direct labor 250,000
Variable Overhead 275,000
Fixed Overhead 600,000 1,625,000
Gross Profit $ 1,875,000
Selling and General & Admin. Exp.
Variable 750,000
Fixed 250,000 1,000,000
Operating Income $ 875,000The break-even point (rounded to the nearest dollar) for Evergreen Corporation for the current year is:
$1,724,138.
$2,625,000.
$2,155,172.
$1,865,672.
The break-even point (rounded to the nearest dollar) for Evergreen Corporation for the current year is: A. $1,724,138.
Break-even pointFirst step is to calculate the Variable costs
Variable costs = $500,000 + $250,000 + $275,000 + $750,000
Variable costs = $1,775,000
Second step is to calculate the Contribution margin ratio
Contribution margin ratio = (Sales - Variable costs) / Sales
Contribution margin ratio= ($3,500,000 - $1,775,000) / $3,500,000
Contribution margin ratio= 0.493×100
Contribution margin ratio =49.3%
Now let calculate the Break-even point
Break-even point = Fixed costs / Contribution margin ratio
Break-even point= ($600,000 + $250,000) / 0.493
Break-even point= $1,724,137.9
Break-even point =$1,724,138 (Approximately)
Therefore the break-even point (rounded to the nearest dollar) for Evergreen Corporation for the current year is:$1,724,138.
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CA is parallel to DE. The measure of BA is 120. The measure of BC is 180. The measure of BD is 80. What is the measure of BE?
A) 60
B) 80
C) 100
D) 120
The measure of BE is 100
Sure hope this helps you
XO
0
1
2
3
4
5
6
f(x)
15
20
25
30
35
чо
45
Answer:
56
Step-by-step explanation:
Solve: x = 27
A) X= 3
B) X = 3 and x = -3
C) X = 9
D) X = 9 and x = -9
Answer:
A) x=3
Step-by-step explanation:
I guess it's : [tex]x^{3} =27[/tex]
[tex]x^{3} =27[/tex]
[tex]x=\sqrt[3]{27}[/tex]
[tex]x = 3[/tex]
An auto weighing 2,000 pounds is on a street inclined at 10° with the horizontal. Find the force necessary to prevent the car from rolling down the hill. (Round your answer to the nearest whole number.)
347 pounds
14,397 pounds
2,462 pounds
Force (F) = WSin(angle)
F = 2000×Sin(10)
Therefore, F = 347lb.
Every year in Delaware there is a contest where people create cannons and catapults designed to launch pumpkins as far in the air as possible. The equation y = 15 + 110x – 16x2 can be used to represent the height, y, of a launched pumpkin, where x is the time in seconds that the pumpkin has been in the air. What is the maximum height that the pumpkin reaches? How many seconds have passed when the pumpkin hits the ground? (Hint: If the pumpkin hits the ground, its height is 0 feet.)
Answer:
See below
Step-by-step explanation:
y = - 16x^2 + 110x + 15 is a dome shaped parabola
max will occur at x = -b/2a = - 110/(2*-16) = 3 7/16 seconds
using this value in the equation results in y = 204 units (feet?)
Height = 0 = -16x^2 +110x + 15 use quadratic formula
with a = -16 b = 110 c = 15 to find 7 seconds
Confirmed as of 12.14.22
Here you go! Please mark Brainliest! Tysm if you do and have a great holiday!
__________
1. $11.50
2. Distributive Property
3. x ->-4 and x -< 3
4. x = 0 or x = -3/2
5. D = all real numbers
R = {y | y -> 0}
6. y = 12/13x - 10/13
slope: 12/13; y-intercept: -10/13
7. y - 3 = 4/9 (x - 9)
8. (1/4, -7); x = 1/4; translated to the right 1/4 unit and down 7 units.
9. Graph C (representing the inequality y -< x/2 - 3)
10. Graph C (representing the system {x -> 0, y -< -1/8x + 5, y -> 5/8x - 1)
11. [ -12 -13 13 | -15]
[ 7 -10 -3 | 11]
[ 7 14 5 | -5]
12. Graph C (representing y = 3(x - 3)^2 + 3)
13. The pumpkin's maximum height is 204.06 feet and it hits the ground after 7.01 seconds.
14. 4x^2 + 3x - 6
15. 7/2 -+ sqrt17/2
16. -15
17. (0,3), (3,0)
18. -3. -2. 2
19. Graph C (Goes vertically down, up, then down again.)
20. -6, -2
21. 2, -2, 4i, -4i
22. s^4 + 15s^4 v + 90s^3 v^2 + 270s^2 b^3 + 405sv^4 + 243v^5
23. y = x - 2
24. f(x) = 295(1.07)^x; 338
25. y = 497(1/2)^38x; 462.029 kg
26. 4
27. 1.03
28. 4.55
29. r = Q/8s^2
30. x = 2
31. Constant of variation: -1/3
x = -63
32. (-1, 7, 5)
33. (x + 4)(6x + 7
______________________________________________
Select the correct answer.
The numbers of pages in the books in a library follow a normal distribution. If the mean number of pages is 180 and the standard deviation is 30
pages, what can you conclude?
OA About 60% of the books have fewer than 150 pages.
O B.
About 16% of the books have fewer than 150 pages.
OC.
About 95% of the books have more than 150 pages.
OD. About 16% of the books have more than 150 pages.
Answer:
B
About 16% of the books have fewer than 150 pages.
Step-by-step explanation:
Quizlet also said so
Evaluate the expressions.
(-7)⁰ = 0
0
2²( ³ ) = 0
5
010
X
Ś
Answer:
[tex]format \: examples \: )[/tex]
(30-30) = 40 RIGHT THE SIMILAR FROM 60 -40 AND CALCULATE ALL OF IT +4
ANSWER: 405
Write the next whole number after 111 in the base-two system.
Answer:
111 (base 8) = 64 +8+1 =73(base10)
111 (base 2) = 4+2+1 =7(base 10)
Sum =73+7=80 (base 10)
8| 80|
8 | 10 | 0
8 | 1 | 2
8| 0 | 1
= 120 (base8)
80 (base10) = 120 (base 8)
Step-by-step explanation:
mark as brilliant
The next whole number after 111 in the base-two system is 1000.
What is the next whole number after 111 in the base-two system.In the base-two system (binary), the numbers are represented using only 0 and 1. After 111 in the base-two system, the next whole number is 1000.
To convert 1000 from base-two to base-ten (decimal), we can calculate as follows:
1 * 2^3 + 0 * 2^2 + 0 * 2^1 + 0 * 2^0 = 8 + 0 + 0 + 0 = 8
So, the next whole number after 111 in the base-two system is 1000.
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Translate "the sum of 6 and the product of 8 and x" into a mathmatical expression
Answer:
6 + 8x
Step-by-step explanation:
Which sentence illustrates the distributive property
Answer:
4th option
Step-by-step explanation:
the distributive property is
a(b + c) = ab + ac
that is each term in the parenthesis is multiplied by a
Answer:
a(b+c)=ab+ac
Step-by-step explanation:
The distributive property is when it distributes the outside variable with whatever is in the parenthesis.
For example, 2(1+3) is 2(1)+2(3)= 2+6=8.
Markson and Sons leases a copy machine with terms that include a fixed fee each month plus a charge for each copy made. Markson made 8,000 copies and paid a total of $980 in January. In April, they paid $760 for 6,000 copies. What is the variable cost per copy if Markson uses the high-low method to analyze costs? If required, round your answer to two decimal places.
The variable cost per copy if Markson uses the high-low method to analyze costs. will be $0.11.
How to calculate the cost?It should be noted that the variable cost per unit will be calculated as:
= Difference in cost between high and low level activities / Difference in units
= (980 - 760)/(8000 - 6000)
= 220/2000
= 0.11
Therefore, the variable cost per copy if Markson uses the high-low method to analyze costs. will be $0.11.
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The rectangle shown is rotated about line k.
Rectangle A B C D is shown. A line of rotation goes through the midpoint of sides A B and D C to cut the side into two equal lengths of 5 inches. Side A D has a length of 4 inches.
What is the approximate base area of the resulting figure?
Area of a circle: A = πr2
31 sq. in.
50 sq. in.
79 sq. in.
314 sq. in.
The approximate base area of the resulting figure is 79 in²
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The resulting figure formed from the rotation is a cylinder with a radius of 5 inches and height of 4 inches
Area of base = π * radius² = π * 5² = 79 in²
The approximate base area of the resulting figure is 79 in²
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In the cycle-plane, what is the y-intercept of the graph of the equation y=6 (x-0.5) (x+3)
The y-intercept of the graph of the equation y = 6 (x - 0.5) (x + 3) will be negative 9.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.
The parabolic equation of the function is given below.
y = 6 (x - 0.5) (x + 3)
Then the y-intercept of the graph of the equation y = 6 (x - 0.5) (x + 3) will be
We know that for the y-intercept, the value of x is zero. Then we have
y = 6 (x - 0.5) (x + 3)
y = 6 (0 - 0.5)(0 + 3)
y = 6 (-0.5)(3)
y = -9
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suppose y varies inversely as x and y=12 when x=6 find y if x=8
Answer:
y = 9
Step-by-step explanation:
given that y varies inversely as x then the equation relating them is
y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation
to find k use the condition y = 12 when x = 6
12 = [tex]\frac{k}{6}[/tex] ← multiply both sides by 6 to clear the fraction
72 = k
y = [tex]\frac{72}{x}[/tex] ← equation of variation
when x = 8 , then
y = [tex]\frac{72}{8}[/tex] = 9
What are the values of x and y?
Figure and answers shown below.
Answer:
C) x = 8√3 ; y = 4√3
Step-by-step explanation:
In this figure, the triangle is 30°-60° right triangle.
So x/12= 2/√3, y/12 = 1/√3
Answer:
C
Step-by-step explanation:
I need help. This is an ixl
Answer: 2
Step-by-step explanation:
We will first pull the data values.
0, 1, 1, 1, 1, 2, 2, 3, 3, 3, 3
Now, we will find the middle data value. This is the median.
0, 1, 1, 1, 1, 2, 2, 3, 3, 3, 3
/, /, /, /, /, 2, /, /, /, /, /
Our median is 2.
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A rectangle has a width of 46 centimeters and a perimeter of 210 centimeters. What is the rectangles length?
Answer:
59 cm
Step-by-step explanation:
First, we can do 46x2=92 to find one part of the perimeter. 210-92=118. 118/2=59. So the length is 59.
What is (f−g)(x) ?
f(x)=x3−3x2+2x−3
g(x)=4x2−5x+7
Enter your answer in the box.
(f−g)(x)=
Answer:
Step-by-step explanation:
(F-G)(X)=x^4-x^3+2x-6
Which table represents a linear function?
(i’m trying to help my friend pass)
Answer:
if I remember I did this two days ago its was c
what is the answer to thiss
Hi Student!
This question is fairly simple because it gives us an equation and they also give us a value for the variable that is within the equation and they tell us evaluate the expression. So let's plug in the values and solve.
Plug in the values
[tex]m^2 + 5[/tex][tex](9)^2 + 5[/tex]Factor out the exponent
[tex](9*9) + 5[/tex][tex]81 + 5[/tex]Combine
[tex]86[/tex]Therefore, the final answer that we would get when substituting m with 9 in the given equation is that we get 86.
Which of the following is the solution to the
inequality below?
-4x-7<5
A. x>-1
B. x < -¹/
C. x>-3
D. x<-3
Answer:
the answer to this problem Is C. x>-3
A skydiver is falling at a rate of 1.1 × 10 2 miles per hour. About how long will it take him to fall 5 miles?
Answer:
See below
Step-by-step explanation:
distance / rate = time
5 miles / 110 m/hr = .04545 hr = 2.727 min = 2 min 44 sec = 1/22 hr
What is the distance between the points (-4,-8) and (6,16), to the nearest tenth of a units?
A. 8.2 units
B.676.0 units
C.21.8 units
D.26.0 units
Answer:
D.26.0 unitsStep-by-step explanation:
Given : the points A(-4,-8) and B(6,16),
Let d be the distance between A and B.
Then
[tex]d=\sqrt{\left( 16-\left( -8\right) \right)^{2} +\left( 6-(-4)\right)^{2} }[/tex]
[tex]=\sqrt{\left( 24\right)^{2} +\left( 10\right)^{2} }[/tex]
[tex]=\sqrt{676 }[/tex]
[tex]=26[/tex]
NO LINKS!!! Please help me with this problem
Answer:
1. 0.75
2. 0.15
3. 1
Step-by-step explanation:
1. P(student is female) = 1 - 0.25 = 0.75
2. P(student is male and does not walk to school) = 0.25 × 0.6 = 0.15
3. P(student walks to school or does not walk to school) = 0.4 + 0.6 = 1
Answer:
The sum of the probabilities of all possible outcomes is 1.
Given:
Male students = 25% = 0.25Students who walk to school = 40% = 0.4Therefore:
Female students = 1 - 0.25 = 0.75Part (a)
[tex]\begin{aligned}\sf P(\textsf{female}) & = 1 - 0.25\\ & = 0.75\\ & = 75\%\end{aligned}[/tex]
Part (b)
[tex]\begin{aligned}\sf P(\textsf{does not walk to school}) & = 1 - 0.4\\ & = 0.6\\ & = 60\%\end{aligned}[/tex]
[tex]\begin{aligned}\implies\sf P(\textsf{student is male and does not walk to school}) & = 0.25 \times 0.6\\ & = 0.15\\ & = 15\%\end{aligned}[/tex]
Part (c)
[tex]\begin{aligned}\implies\sf P(\textsf{student walks to school or does not walk to school}) & = 0.4+0.6\\ & = 1\\ & = 100\%\end{aligned}[/tex]
Two spheres have volumes of 87pi cm³ and 64pi cm³. If the surface area of the smaller sphere is 16pi cm², what is the
surface area of the larger sphere?
O 64pi cm²
O 96pi cm²
O 128pi cm²
O 256pi cm²
The surface area of the large sphere is 128π cm²
Complete questionTwo spheres have volumes of 8π cm3 and 64π cm3. If the surface area of the smaller sphere is 16π cm2, what is the surface area of the larger sphere?
How to determine the larger area?The given parameters can be represented using the following ratio:
Small Area : Large Area = Small Volume : Large Volume
Substitute the given parameters
16π : Large Area = 8π : 64π
Express as fraction
Large/16π = 64π/8π
Multiply both sides by 16π
Large = 128π
Hence, the surface area of the large sphere is 128π cm²
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Question 6 of 10
Estimate the sum of the decimals below by rounding to the nearest whole
number. Enter your answer in the space provided.
6.833
3.594
+1.369
————
Answer here
Step-by-step explanation:
7
4
1
----
12
reality
6.833
3.594
1.369
----------
11.796
Determine whether or not the situation describes a function. Give a reason for your answer. The letter grade in this course is a function of your numerical grade. a. No, it is not a function. Each letter grade corresponds to one numerical grade. b. No, it is not a function. Each numerical grade corresponds to one letter grade. c. Yes, it is a function. Each numerical grade corresponds to one letter grade. d. Yes, it is a function. Each letter grade corresponds to one numerical grade. Please select the best answer from the choices provided A B C D
Yes, it is a function. Each numerical grade corresponds to one letter grade. Then the correct option is C.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.
Determine whether or not the situation describes a function.
The letter grade in this course is a function of your numerical grade.
Yes, it is a function. Each numerical grade corresponds to one letter grade.
Then the correct option is C.
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Help Me please . I want to know cube root of 512 and 997002999 . please man fast
Answer:
8,999
Step-by-step explanation:
Cube root of 512 is 8.
cube root of 997002999 is 999.